Of Mites and Men: Johannes Kepler on Stars and Size (with an English translation of Chapter 16 of his 1606 De Stella Nova) Christopher M. Graney Jefferson Community & Technical College Louisville, KY 40272 [email protected] ABSTRACT: In his 1606 De Stella Nova, Johannes Kepler attempted to answer Tycho Brahe’s argument that the Copernican heliocentric hypothesis required all the fixed stars to dwarf the Sun, something Brahe found to be a great drawback of that hypothesis. This paper includes a translation into English of Chapter 16 of De Stella Nova, in which Kepler discusses this argument, along with brief outlines of both Tycho’s argument and Kepler’s answer (which references snakes, mites, men, and divine power, among other things). Page 1 of 19 Page 2 of 19 ycho Brahe had developed a strong objection to the heliocentric theory of Nicolaus Copernicus. Johannes Kepler set out to answer that objection in his 1606 book De Stella T Nova, his book on the “new star” of 1604 (now known to have been a supernova). Brahe’s objection was rooted in the stars. In the heliocentric theory the stars had to be very distant in order to explain why Earth’s annual motion around the Sun produced no corresponding visible annual changes in their appearance—no “annual parallax”. For instance, stars were not seen to grow brighter when Earth happened to move toward them as it journeyed around the Sun, nor were they seen to grow dimmer when it moved away from them. The explanation for this was that the orbit of the Earth was like a point in comparison to the distance to the stars— negligible in size. But Brahe noted that stars have a measurable apparent size as seen from Earth. He had measured these sizes. He determined that the more prominent or “first magnitude” stars measured a little less than a tenth the apparent diameter of the Moon—a little less than three minutes of arc, since the Moon has an apparent diameter of approximately thirty minutes, or one half of one degree. At the vast distances required for the stars in the heliocentric hypothesis, these apparent sizes translated into enormous physical sizes. Were Copernicus correct, every one of the stars would have to dwarf the Sun. The Sun would be a unique, small body in a universe of giants.1 A decade after Brahe died, Johann Georg Locher and his mentor Christoph Scheiner would neatly summarize Brahe’s objection in their 1614 book Disquisitiones Mathematicae. They wrote that in the Copernican hypothesis the Earth’s orbit is like a point within the universe of stars; but the stars, having measurable sizes, are larger than points; therefore, in the Copernican hypothesis every star must be larger than Earth’s orbit, and of course vastly larger than the Sun itself.2 The giant stars of the Copernican hypothesis stood in contrast to the more commensurate star sizes found in Brahe’s own hypothesis, a hybrid geocentric (or geo-heliocentric) hypothesis in which the Sun, Moon, and stars circled an immobile Earth, but the planets circled the Sun (Figure 1). Brahe’s hypothesis was observationally and mathematically identical to the Copernican hypothesis insofar as the Sun, Moon, and planets were concerned. However, since the Earth did not move relative to the stars in Brahe’s geocentric hypothesis, there was no expectation of annual parallax, and thus no need for the stars to be distant in order to explain the absence of observable parallax. Brahe had the stars located a bit beyond Saturn. And, since the stars were roughly similar to Saturn in both distance and in their appearance in the night sky, they had to be similar to Saturn in physical size, too. In Brahe’s hypothesis, the sizes of the Earth, Sun, Moon, and planets were commensurate, with the Moon being smallest and the Sun being largest, as opposed to the case in the Copernican hypothesis, where every last star dwarfed Sun, Moon, and planets (see Figure 2).3 1 (Graney 2015, 32-38) 2 (Graney 2017, 30) 3 (Graney 2015, 32-38) Page 3 of 19 Kepler devotes Chapter 16 of De Stella Nova to the star size issue. This follows a discussion of the vast distance of the stella nova from Earth in Chapter 15. A translation of Chapter 16 into English is provided here in Appendix 1. The historian of science Albert van Helden has written that Brahe’s measurements of the apparent sizes of stars were unassailable, and his logic incontrovertible, so Copernicans simply had to accept Brahe’s objection and agree that the stars were giant.4 This Kepler does. He does not question that the stars are all vastly larger than the Sun. In fact, in Chapter 16 he grants that a star with an apparent diameter of three minutes, one tenth the diameter of the Moon, has the same physical size as the orbit of Saturn; and that Sirius, the most brilliant of stars, is even larger; and the nova larger still. It follows from Kepler’s numbers that any star whose physical size was the same as Earth’s orbit would have an apparent diameter of three tenths of a minute, or eighteen seconds, the apparent diameter that Brahe had determined for the stars barely visible to the eye (sixth-magnitude stars).5 And as the physical diameter of the Sun is less than one hundredth that of Earth’s orbit according to Kepler, clearly every last star in the sky utterly dwarfs the Sun. To Kepler, the Sun and its planets are surrounded by giants, and only by giants. Kepler’s answer to Brahe then is that the Sun and planets being surrounded by giants makes sense, or at least more sense than the geocentric alternative. Kepler argues that Brahe fixes upon size, but that what is commensurate in the Copernican hypothesis are speeds. Speeds in any geocentric hypothesis are more incommensurate than sizes in the heliocentric hypothesis, he says. Moreover, he says, a vast range of sizes exists in the physical world, and he illustrates some of these: the longest snake vs. the smallest insect; human beings vs. the Earth; the Earth vs. the universe. And finally, there is the power and creativity of God, for whom nothing is too big, and yet who also confers value upon the small. Answers such as these to Brahe’s star size objection to Copernicus would endure. In 1651 Giovanni Battista Riccioli in his Almagestum Novum analyzed one hundred and twenty six pro- and anti-Copernican arguments, concluding that the vast majority in either direction were indecisive. As he saw it, there were two decisive arguments, both in favor of the anti- Copernicans: one was the absence of any detectable Coriolis Effect (as it would be called today);6 the other was Brahe’s star size objection. By 1651 the telescope had long been brought to bear on the star size question, including by Riccioli,7 but since the small-aperture telescopes of the time showed stars as definite disks (not yet understood to be spurious artefacts of diffraction; see Figure 3) but did not reveal any parallax, Brahe’s objection still stood (Simon Marius in his 1614 Mundus Jovialis first noted this telescopic support for Brahe8). Riccioli noted how Brahe’s objection could be answered by appealing to the speed issue, but he dismissed this answer. The rising and setting of the stars is caused by either the rotation of the Earth or the rotation of the stars, he said, and in either case, whatever rotates turns though one circumference per day— 4 (Van Helden 1985, 51) 5 (Graney 2015, 34) Brahe reported sixth-magnitude stars as having a diameter of twenty seconds. 6 (Graney 2015, 115-128), (Graney 2017, xix) 7 (Graney 2015, 53-61, 129-139) 8 (Graney 2015, 50-53) Page 4 of 19 proportionally the rates of motion are the same. And as for appealing to the power of God, that answer cannot be refuted, said the Jesuit Riccioli, but it does not satisfy the prudent. Besides, he said, if divine power can be called in as an explanation for the difficult aspects of a hypothesis, could not the geocentric hypothesis’s vast speeds also be explained via divine power?9 Thus whereas Johannes Kepler set out in De Stella Nova to answer Tycho Brahe’s star size objection to the heliocentric theory of Nicolaus Copernicus, that objection still carried force almost five decades later. What would answer Brahe’s objection would not be comparisons to geocentric speeds, or discussions of the sizes of snakes and mites, or appeals to divine power. Rather it would be the discovery that the apparent sizes of stars, whether measured visually or with a telescope, were the spurious product of optical systems, a product which gave no indication of the true sizes of stars. The first evidence suggesting the spurious nature of apparent stellar sizes, Jeremiah Horrocks’ observations that stars winked out instantaneously when being occulted by the Moon, was not published until a decade after Riccioli’s Almagestum Novum, six decades after De Stella Nova.10 Such evidence would eventually show that stars did not have to all be giants in a Copernican universe. Indeed, recent progress in astronomy has shown that, while some giant stars do exist that dwarf the sun, these are relatively rare; most stars are smaller than the Sun, with a large majority of stars being small, dim “red dwarfs” that are far outclassed by the Sun. 9 (Graney 2015, 136-138) 10 (Graney 2015, 150-151) Page 5 of 19 Page 6 of 19 APPENDIX 1—A translation into English of Chapter 16 of Johannes Kepler’s De Stella Nova.